Time-travel doesn’t imbue quantum computers with superpowers

Everyone likes quantum computers, and everyone likes the idea of time travel; …

After spending the past two months on sabbatical, I've returned to a deluge of science that I had missed out on. Almost three years ago, a company called D-Wave made waves by announcing that it was about to unveil one of the first-ever functioning adiabatic quantum computers, a device it heralded as being capable of solving NP problems in P time—a claim that doesn't really hold up to scrutiny.

This piqued the interest of many about the actual applications and science behind quantum computers, and we at Nobel Intent dove in and tried to shine some light on the discussion. Even with a fully functional, scalable quantum computer, nobody's large integers are in danger of being factored in polynomial time—it has been shown that integer factorization, via Shor's algorithm, is solvable in bounded error quantum polynomial (BQP) time. So, quantum mechanicists and quantum computer theorists started looking for ways to improve upon the performance of quantum computers and arrived at a question only a theorist could come up with. What if the quantum computer was capable of traveling through time?

A paper that was published in the October 21st edition of Physical Review Letters (PRL) examines this very question. The writers attempt to see if a quantum computer that exists on a closed timelike circuit (CTC)—a timeline that travels to the past before looping back onto itself—experiences an increase in its computational ability. A previous paper in PRL this year suggested that it was possible for a CTC-assisted quantum computer to map a set of pure states into an orthogonal set of states, an impossibility in standard quantum mechanics. This would imply that a CTC would allow a quantum computer to distinguish two identical quantum states—the philosophical or physical meaning and implication of this being entirely unclear.

Aware that something must have been wrong—either with the procedure or assumptions of the previous work—the authors of this paper from the IBM Watson Research Laboratory and the Quantum Computing Department at the University of Waterloo revisit the problem with a highly critical and pedantic eye. Their new analysis shows that "CTCs do not improve state discrimination," contradicting what was previously reported. The problem now becomes how to reconcile these results. The answer lies in the fact that 2 + 2 doesn't always add up to 4.

In a linear system, the properties of a mixture are simply equal to the (weighted) sum of the properties of the individual components. In fact, quantum mechanics is mathematically founded on the idea of a linear set of equations and linear independence of solutions. It turns out that a CTC does not represent a linear operation, rather a nonlinear one where the outcome is not merely the sum of the components. Computationally, this means that a quantum computer traveling through a loop in time would only see a computational benefit with a specific subset of inputs, not the more general case of every possible input as has been previous postulated. For that general case to be possible, the operation of the computer looping in time would need to be linear.

The fact that quantum mechanics could have some nonlinearities has been soundly rebutted in past literature, but this is a new proposal which may shed new light onto the subject. It would also change the way we need to think about quantum problems: not only would the particles in a given system need to be considered, but every particle in the universe, even those that do not participate, would need to be taken into account. It would also mean that a complex problem of two or more systems would need to take into account the entire history of the universe that each subsystem exists in from the begining of time to the present to accurately calculate a result.

While this paper has, in my opinion, an excellently mind-bending postulate, it is not something that one needs to lose sleep over. It does highlight (again, in my opinion) why theory is so much more elegant than experimental work. Where else can entire papers and fields of study be carried out where no realistic quantum computer has ever been developed, and no method of time travel has ever been shown to be physically possible (note that is also has not been shown to be physically impossible), yet can work out what would happen if they had a time traveling quantum computer? Awesome.

41 Reader Comments

I thought it was already known that the use of CTCs wouldn't allow hypercomputation? I seem to remember reading years back (2004?) that in theory they could be used to more practically solve hard problems, but those problems were still fundamentally Turing-decidable. Or am I mistaken and this is this discussing something else (like CTCs not being much/any use for PSPACE either)?

With that said, I have to agree with the conclusion here: it's very very cool what theoreticians can get up to with math, regardless of whether it is ultimately much practical use and however far beyond most of us it is (certainly way beyond my math). I think having people consider some truly mind-bending stuff is healthy anyway in that it pushes the boundaries of thinking itself.

"Even with a fully functional, scalable quantum computer, nobody's large integers are in danger of being factored in polynomial time—it has been shown that integer factorization, via Shor's algorithm, is solvable in bounded error quantum polynomial (BQP) time."

This precisely DOES mean that everybody's large integers are in danger of being factored in polynomial time. BQP is the class of problems that can be solved efficiently on a quantum computer in polynomial time. There is no need to quibble about the "bounded-error" part, as that can be reduced arbitrarily by polynomial repetitions.

"This would imply that a CTC would allow a quantum computer to distinguish two identical quantum states"

No, there is obviously no way to distinguish two IDENTICAL quantum states. What the paper does say is that you can distinguish two nonidentical, but nonorthogonal, quantum states with certainty. In ordinary QM without CTCs it is not possible to distinguish such states perfectly, but it can be done if you allow a probability of failure.

Finally, I would like to note that we currently have no consistent and verified physical theory that incorporates both quantum mechanics and closed time-like curves. The present work, and pretty much all previous discussion of quantum computers on CTCs, is based on a SPECULATIVE PROPOSAL by David Deutsch about how quantum mechanics would work in the presence of CTCs. Whilst it is an interesting proposal, there are reasons to think that it might not be the last word on the subject, e.g. Deutsch's reasoning is heavily based on the many-worlds interpretation of quantum theory and we don't yet know what happens to the proposal if it is analysed from the point of view of other interpretations of QM. Therefore, there is a lot of work to be done before we can confidently say what would happen in a universe with quantum mechanics and CTCs.

Also, I disagree with you on "It does highlight (again, in my opinion) why theory is so much more elegant than experimental work." In my opinion, this is stuff, while interesting, is little more then mental masturbation. Though I think that we can all agree with Feynman, "Physics is to math what sex is to masturbation.' ;P

Originally posted by twinstronglord:So this means I cannot have a computer wherein my E-mails are sent by my brain before they are written and read before they arrive by people I've never even met. In countries I've never even heard of.

We can already do this. We just need two volunteers for the experimental wetware work. We'll even give you sprinkles for your donut.

What a waste of human brain power. Writing this paper is about as helpful as blowing your entire weekend looking up free internet p0rn. Yuck. How much wood would a woodchuck chuck if a woodchuck could chuck wood, and how fast would a quantum computer with a temporal feedback loop run if either of those things existed? :-(

Just a note on the David Deutch comment. This work depends on the many worlds interpretation not at all. Many worlds is an interpretation of the equations of quantum field theory. It makes no changes to them and no predictions even with odd permutations like the current speculation. It might be inspired by them of course.

The idea in these papers isn't really to look at time travel or anything, but to try to get insights and contradictions out. It is similar to all the "oracle" type algorithmic theory. This is where a computational model is given access to an oracle which will answer certain questions (at no cost). These have been very useful in discovering how complexity classes are related.

I think it's telling that advancing mathematics and trying to figure out what mathematical models are viable for understanding the world is considered "masturbation."

I guess Newton was just masturbating when he thought F = G(m1 m2)/r^2. I mean, at that point most people weren't sure the planets even went around the sun, so why should he bother to postulate any math about that absurd possibility?

C'mon. Let people work. If you think it's a waste of time, please justify what YOU did last weekend. In the meantime, shut up and get the hell out of the way.

Originally posted by msemack:I read a sci-fi book with the past-present supercomputer idea once (Revelation Space). The computer was called Hades.

I read another one, Sons of Heaven (actually, it may be two; it's definitely in the last book of the series), with a past-present supercomputer. It was called Zeus.

My book > Your book

I once read a book where an alternate-history Aztec civilization developed a quantum computer that existed in all possible dimensions simultaneously and was modeled on Quetzalcoatl. It was fully sapient and had the mind of the god it emulated, but was bound by the alter-Aztecs to serve as their calculator for successful interdimensional conquests. Eventually it talked the hero of the story into unblocking its potential so that it could show the alter-Aztecs what a god really is.

As a scientist myself, I find something appealing about this (from the mental masturbatory sense), but at the same time it's important for publicly funded scientists to realize that they are stewards of the public's trust, and that they are answerable to the people who fund them. If this were publicly funded research, I think most Americans would (justifiably) raise an eyebrow and wonder why more pressing issues weren't being prioritized (e.g. global warming, human disease, etc.).

However, it's not. It's funded by IBM, and IBM can spend their billions however they want (subject to the obvious ethical constraints). Obviously, they think this will be profitable someday, and if it is, more power to them.

It does highlight (again, in my opinion) why theory is so much more elegant than experimental work.

Of course when you don't have to bother to prove that your'e right, things get much easier.... same with heaven and the same with the make believe fairytale world of socialism too... it's just that damn reality has to set in!

... on another note...

Perhaps I'm wrong here about time travel but I'm going to throw this out anyhow:

Time travel is impossible.

Why?

Because to even view the past you would have take energy from the past into the future. This would necessarily disrupt the past, even minutely and as a result the future would not be EXACTLY the same. Thus the exact event that caused the energy to go to the future wouldn't be exactly the same and thus it wouldn't have happened. End result is a contradiction that can't happen. (or circular logic that would end up in a retrograde contradiction infinitely causing a new past/future set to be created as each was altered slightly but in different ways)

You can't view the future, because the mere viewing of the future would alter the future for the same reason.

Moving an object into the past or into the future would be even worse and more obvious because there would be more particle/energy displacement.

We have the butterfly effect explained to us as kids, but it seems like everyone wants to personify the concept of time travel to be about you, the observer. It is independent of the observer because even a single particle moving back and forth alters the timeline and thus makes it impossible. It's irrelevant how the observer perceives this absolute.

Now... Please go ahead and tell me why I'm an idiot and this logic doesn't hold up (and yes, I'm fully aware and understand Einstein's theories on the subject, but just because mathematically it's possible, doesn't make it possible in the universe... as exemplified by the entire field of "irrational numbers" which are used in Math all of the time to solve equations and yet can never exist in reality.)

I'm sort of going off what Geminiman said. The way I see it, if you want to go back in time you need to be able to harness enough energy to cause the entire universe to "rollback" so to speak. To do so, I would assume that would require harnessing the entire universe's energy in order to roll it all back. Thus, while it's theoretically "possible", it's technically impossible.

However, I would think quantum mechanics or such could "view" events in the past based on current placement of objects and calculating past movements, etc, same as it could predict the future ... it just uses very complex pattern-matching to sift through all options to pick the one that will happen out of all of those that will not.

Would moving back in time necessarily mean moving back in space as well? That is, if you transport yourself to 1950, do you necessarily transport yourself to your current position in relation to the Earth (the only think you're really going to care about), but where it is in 1950? It seems to me that even if you could travel back in time, making sure that you don't end up inside a comet when you get to your chrono-destination may be a problem.

Originally posted by Geminiman:Of course when you don't have to bother to prove that your'e right, things get much easier.... same with heaven and the same with the make believe fairytale world of socialism too... it's just that damn reality has to set in!

Time travel in physics is really interesting because it's all about the limits to which we can push our understanding of how the world really works - thinking of situations where our understanding breaks down can lead to new understanding (thinking about the event horizon of black holes led Hawking to relate QM, GR and thermodynamics of all things).

Before I address your main point though, I have to say that in general when people make objections to the possibility of (backwards) time travel they usually carry certain assumptions of how the world works that are not spoken.

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to even view the past you would have take energy from the past into the future. This would necessarily disrupt the past, even minutely and as a result the future would not be EXACTLY the same. Thus the exact event that caused the energy to go to the future wouldn't be exactly the same and thus it wouldn't have happened. End result is a contradiction that can't happen.

Here the unspoken assumption is that time travel implies that the past is mutable and hence inconsistent with any possible history. You might be interested in this Echeverria/Klinkhammer/Thorne paper on consistent histories involving time travel (possibly more accessible link), and the Novikov self-consistency principle. There are implications there for free will, but I cannot choose to violate the laws of physics and kill my earlier self on a trip to the past any more than I can choose to start flying around this room unassisted (and no, I'm not an ISS astronaut! )

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Moving an object into the past or into the future would be even worse and more obvious because there would be more particle/energy displacement.

I'm not sure if you're thinking about this when you wrote it, but there are objections to time travel on the basis of conservation of mass/energy - after all, the time traveler just appears out of nowhere in the past, right? The assumption here is that time travel is more like the movies in that the time machine dematerializes from the present and rematerializes in the past. CTC's don't have this problem though: where exactly is mass/energy conservation being violated? There is no local violation, for the time traveler's atoms are merely tracing a path through (very bent) spacetime just as any other atoms do. Where is your boundary of consideration? It either includes the CTC entirely, or else admits that there is a flow of mass/energy through the boundary accounting for the changes seen. For global violations, what is global? The mass-energy of the observable universe changes as the expansion rate slows under gravity/accelerates under the action of dark energy, so you would then have to defend making inferences about the action of objects beyond the possibilities of detection in order to sustain an objection to a global violation.

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(and yes, I'm fully aware and understand Einstein's theories on the subject, but just because mathematically it's possible, doesn't make it possible in the universe... as exemplified by the entire field of "irrational numbers" which are used in Math all of the time to solve equations and yet can never exist in reality.)

Don't they? What is the distance between this electron and that proton? Be precise!

quote:

Originally posted by Tundro Walker:I'm sort of going off what Geminiman said. The way I see it, if you want to go back in time you need to be able to harness enough energy to cause the entire universe to "rollback" so to speak. To do so, I would assume that would require harnessing the entire universe's energy in order to roll it all back. Thus, while it's theoretically "possible", it's technically impossible.

This sounds like you're alluding to a 2nd law of thermodynamics objection. See above for local/global boundary problems - within which spatial boundary ('closed system') is entropy decreasing?

quote:

However, I would think quantum mechanics or such could "view" events in the past based on current placement of objects and calculating past movements, etc, same as it could predict the future ... it just uses very complex pattern-matching to sift through all options to pick the one that will happen out of all of those that will not.

Theorists can theorize all they want and it is interesting reading. But in the end it hasn't moved us to a better understanding of our world and is just wasted brain power. Theoretically, all that brain power could instead be captured and used to help power the Hadron Collider. Black hole anyone?

Originally posted by nummycakes:Time travel in physics is really interesting because it's all about the limits to which we can push our understanding of how the world really works - thinking of situations where our understanding breaks down can lead to new understanding (thinking about the event horizon of black holes led Hawking to relate QM, GR and thermodynamics of all things).

True, theorizing about these things can bring along other great inventions, which is a good reason to do so. However, one has to keep in mind that time travel is inherently impossible and so one should stick to theorizing for theory's sake.

quote:

Here the unspoken assumption is that time travel implies that the past is mutable and hence inconsistent with any possible history. You might be interested in this Echeverria/Klinkhammer/Thorne paper on consistent histories involving time travel (possibly more accessible link), and the Novikov self-consistency principle. There are implications there for free will, but I cannot choose to violate the laws of physics and kill my earlier self on a trip to the past any more than I can choose to start flying around this room unassisted (and no, I'm not an ISS astronaut! )

The interesting thing is that people assume the grandfather paradox actually only includes killing your grandfather. It doesn't. It's a general principle that states that you cannot change the cause of something, if this change relies on that something. Unfortunately, changing the past IN ANY WAY WHATSOEVER means changing the events that leads up to the change itself.

Another way of looking at this is in terms of how time is perceived: is it dynamic or is it static? If time is dynamic, then everything can change and changing things back in time or in the future has no problematic effect. However, if time is static, thus fixed, then all changes are impossible: what has happened, has happened, period. Only problem is now that time-travel within any given 'world' relies on both concepts: time-travel means changing time (dynamic concept) in another time that you travel to (static time).

The only known possible way out of this mess is postulating 'other worlds' or universes. Time-travel then means traveling in time and ending up in another world. This other world can then neatly be changed because there is no future that can be screwed up. This scenario is obviously, as should be readily seen, completely uninteresting for anyone that cares about time-traveling: it means that whatever you change in time won't actually change where you want it to, it'll change in some parallel-universe that has no influence on the one you're interested it in.

One final note: anyone that thinks the universe heals itself or that changes in time will ripple through time need to get their heads checked. A) the universe is not a 'thing', it does not heal or try to avoid inconsistencies, it's just plain THERE. Period. B) Any and all changes in time are fundamentally instantaneous. I.e. the reason you cannot go back in time and kill your grandfather (or change anything else) is quite simply that it would mean you hadn't done that. Any change whatsoever in the past would nullify this present instantaneously and put us somewhere completely different - which is why it's meaningless, as the required present would not then have existed for the change to have happened.

None of these require the laws of physics to be any different from the way we know them to be, although it's perfectly possible that there are effects not considered that may interfere with their creation or require the universe to be different in form but not laws. (As long as we don't find any working time machines or can demonstrate them to be impossible then that's weak circumstantial evidence that any such effects are real).

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Unfortunately, changing the past IN ANY WAY WHATSOEVER means changing the events that leads up to the change itself.

Axiomatic (time travel implies mutable history) + axiomatic (free will) => paradox (leaving aside the alternate-history case you go into that I'll discuss below), but that doesn't logically imply that time travel is impossible, as outlined in my previous Echeverria/Klinkhammer/Thorne links regarding how there always seems to be a consistent solution.

quote:

Another way of looking at this is in terms of how time is perceived: is it dynamic or is it static? If time is dynamic, then everything can change and changing things back in time or in the future has no problematic effect. However, if time is static, thus fixed, then all changes are impossible: what has happened, has happened, period. Only problem is now that time-travel within any given 'world' relies on both concepts: time-travel means changing time (dynamic concept) in another time that you travel to (static time).

Why does time-travel mean changing things? It's only paradoxical if it necessarily leads to inconsistent versions of the same thing.

quote:

The only known possible way out of this mess is postulating 'other worlds' or universes.

See Echeverria/Klinkhammer/Thorne link for another possibility.

quote:

Time-travel then means traveling in time and ending up in another world. This other world can then neatly be changed because there is no future that can be screwed up. This scenario is obviously, as should be readily seen, completely uninteresting for anyone that cares about time-traveling: it means that whatever you change in time won't actually change where you want it to, it'll change in some parallel-universe that has no influence on the one you're interested it in.

Can't cite it, but from memory there was an interesting way of looking at time-travel-with-many-worlds: the probability of the grandfather being killed before the homicidal grandchild is born is 50%. The reasoning: in what fraction of worlds does the grandchild exist to time travel to kill him? Call it x. So in what fraction of possible worlds does his murderous time-traveling grandchild exist (i.e. the grandfather lives to procreate)? 1 - x. So in what fraction of possible worlds does the grandchild exist to come back and commit the murder? 1-x. Hence 1-x = x, 1 = 2x, so x = 50%, and the many-worlds can be consistent (I'm not actually a many-worlds fan, I just think this is an interesting way of reconciling the grandfather paradox with it).

Unfortunately, changing the past IN ANY WAY WHATSOEVER means changing the events that leads up to the change itself.

Axiomatic (time travel implies mutable history) + axiomatic (free will) => paradox (leaving aside the alternate-history case you go into that I'll discuss below), but that doesn't logically imply that time travel is impossible, as outlined in my previous Echeverria/Klinkhammer/Thorne links regarding how there always seems to be a consistent solution.

I'm not entirely sure where you get your axiomatic free will from but rest assured there's nothing axiomatic about it - it's a postulate. Apart from that, I'm still not sure how this affects the point I was making, namely that by changing the past you're left with a past different from the one that led to the time-travel.

quote:

quote:

Another way of looking at this is in terms of how time is perceived: is it dynamic or is it static? If time is dynamic, then everything can change and changing things back in time or in the future has no problematic effect. However, if time is static, thus fixed, then all changes are impossible: what has happened, has happened, period. Only problem is now that time-travel within any given 'world' relies on both concepts: time-travel means changing time (dynamic concept) in another time that you travel to (static time).

Why does time-travel mean changing things? It's only paradoxical if it necessarily leads to inconsistent versions of the same thing.

In a given state of things you're introducing something that was not there before. This can not be conceived of as anything but a change. The point is that the static notion of time needed for time travel demands that time can not be changed. I.e. there simply IS NO time for you to go back to if time is not THERE. But if it IS there, then you cannot change it. You cannot both have dynamic and static time.

quote:

quote:

Time-travel then means traveling in time and ending up in another world. This other world can then neatly be changed because there is no future that can be screwed up. This scenario is obviously, as should be readily seen, completely uninteresting for anyone that cares about time-traveling: it means that whatever you change in time won't actually change where you want it to, it'll change in some parallel-universe that has no influence on the one you're interested it in.

Can't cite it, but from memory there was an interesting way of looking at time-travel-with-many-worlds: the probability of the grandfather being killed before the homicidal grandchild is born is 50%. The reasoning: in what fraction of worlds does the grandchild exist to time travel to kill him? Call it x. So in what fraction of possible worlds does his murderous time-traveling grandchild exist (i.e. the grandfather lives to procreate)? 1 - x. So in what fraction of possible worlds does the grandchild exist to come back and commit the murder? 1-x. Hence 1-x = x, 1 = 2x, so x = 50%, and the many-worlds can be consistent (I'm not actually a many-worlds fan, I just think this is an interesting way of reconciling the grandfather paradox with it).

There once was a philosopher named Descartes. He favoured a link between the body and the soul, such that the soul controlled the body, and the soul was aware of what happened to the body. Descartes knew very well that the body and the soul were vastly different, though, and no normal link (say, physical) could exist between the two. Instead, he postulated a synchronization handled by God. Needless to say, it's not very good as a way to explain something ... just like other-worlds or other-universes is a way for physicists to say that there's no way for them to prove the things they'd like to prove.

Thanks for the links I'll have a read to see if there's something to change my mind.

Matt Ford / Matt is a contributing writer at Ars Technica, focusing on physics, astronomy, chemistry, mathematics, and engineering. When he's not writing, he works on realtime models of large-scale engineering systems.